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ldefint gives a wrong answer (basically bug 1044318)

(%i10) ldefint(1/(sin(x)^2+1),x,1,1+%pi);

(%o10) 0

integrate gives an antiderivative that isn't continuous

at odd integer multiples of %pi / 2

(%i11) integrate(1/(sin(x)^2+1),x);

(%o11) atan((2*tan(x))/sqrt(2))/sqrt(2)

The expression

atan(2*tan(x)/sqrt(2))/sqrt(2)+sqrt(2)*%pi*floor(x/%pi-1/2)/2

might be a valid antiderivative on all of R provided the

first term is assumed left continuous at each odd integer

multiple of %pi/2, I think.

Barton